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Compilation Booklet of Past Papers for Paper 3 - Pure Mathematics 2 & 3
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Cambridge International AS & A Level Mathematics 9709: Pure Mathematics 2 & 3 Compilation book of Past Papers for Paper 3 All past papers from 2019 to 2022

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  • January 25, 2023
  • 796
  • 2022/2023
  • Exam (elaborations)
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Cambridge International Examinations
Cambridge International Advanced Level




CANDIDATE
NAME

CENTRE CANDIDATE
*0123456789*




NUMBER NUMBER


MATHEMATICS 9709/03
Paper 3 Pure Mathematics 3 (P3) For Examination from 2017
SPECIMEN PAPER 1 hour 45 minutes
Candidates answer on the Question Paper.
Additional Materials: List of Formulae (MF9)

READ THESE INSTRUCTIONS FIRST

Write your Centre number, candidate number and name in the spaces at the top of this page.
Write in dark blue or black pen.
You may use an HB pencil for any diagrams or graphs.
Do not use staples, paper clips, glue or correction fluid.
DO NOT WRITE IN ANY BARCODES.

Answer all the questions.
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in
degrees, unless a different level of accuracy is specified in the question.
The use of an electronic calculator is expected, where appropriate.
You are reminded of the need for clear presentation in your answers.

At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for this paper is 75.




This document consists of 19 printed pages and 1 blank page.


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1 Solve the inequality 2x − 5 > 32x + 1. [4]

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© UCLES 2016 9709/03/SP/17

, 3

2 Using the substitution u = 3x , solve the equation 3x + 32x = 33x giving your answer correct to 3 significant
figures. [5]

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© UCLES 2016 9709/03/SP/17 [Turn over

, 4

3 The angles 1 and & lie between 0Å and 180Å, and are such that
tan 1 − & = 3 and tan 1 + tan & = 1.
Find the possible values of 1 and &. [6]

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© UCLES 2016 9709/03/SP/17

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© UCLES 2016 9709/03/SP/17 [Turn over

, 6

4 The equation x3 − x2 − 6 = 0 has one real root, denoted by !.

(i) Find by calculation the pair of consecutive integers between which ! lies. [2]

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(ii) Show that, if a sequence of values given by the iterative formula
_P Q
6
xn+1 = xn +
xn
converges, then it converges to !. [2]

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© UCLES 2016 9709/03/SP/17

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(iii) Use this iterative formula to determine ! correct to 3 decimal places. Give the result of each
iteration to 5 decimal places. [3]

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© UCLES 2016 9709/03/SP/17 [Turn over

, 8

5 The equation of a curve is y = e−2x tan x, for 0 ≤ x < 12 0.

dy
(i) Obtain an expression for and show that it can be written in the form e−2x a + b tan x2 , where
dx
a and b are constants. [5]

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© UCLES 2016 9709/03/SP/17

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(ii) Explain why the gradient of the curve is never negative. [1]

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(iii) Find the value of x for which the gradient is least. [1]

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© UCLES 2016 9709/03/SP/17 [Turn over

, 10

6 The polynomial 8x3 + ax2 + bx − 1, where a and b are constants, is denoted by p x. It is given that
x + 1 is a factor of p x and that when p x is divided by 2x + 1 the remainder is 1.

(i) Find the values of a and b. [5]

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© UCLES 2016 9709/03/SP/17

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